1. Limits and Continuity

Working With The Intermediate Value Theorem (ivt) — Quiz

Test your understanding of working with the intermediate value theorem (ivt) with 5 practice questions.

Practice Questions

Question 1

Which condition must be true before the Intermediate Value Theorem can be applied to a function on an interval?

Question 2

Let $f$ be continuous on $[1,5]$ with $f(1)=-2$ and $f(5)=4$. Which value must $f$ take somewhere on $[1,5]$?

Question 3

Suppose $f$ is continuous on $[a,b]$ and $f(a)<0<f(b)$. What does the Intermediate Value Theorem guarantee?

Question 4

Why can the Intermediate Value Theorem not be applied to $f(x)=\frac{1}{x}$ on $[-1,1]$?

Question 5

Let $f$ be continuous on $[0,2]$ with $f(0)=3$ and $f(2)=7$. Which statement is guaranteed?